class Solution {
    public int minInsertions(String s) {
        int len =s.length() ;
        char[] arr = s.toCharArray() ;
        int[][] dp = new int[len][len] ;
        for(int i= len-1 ; i >= 0 ; i --){
            for(int j = i ; j < len ; j ++){
                if(arr[i] == arr[j]){
                    dp[i][j] = i+1 < j ? dp[i+1][j-1] : 0;
                }else{
                    dp[i][j] = Math.min(dp[i][j-1] , dp[i+1][j] )+1 ;
                }
            }
        }
        return dp[0][len-1] ;
    }
}